Therianthropes? Lycanthropes? Animorphs? Homo-Zoological-Hybrid-Sapiens? Manimals? Take your pick.
A culture believes that souls are recycled. One child gets half of a soul, another child gets the other half. However, this means that with each passing generation, the amount of soul in the child will become less and less (Through division)until their culture will die in the future because of their soulless offspring.